IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3330-d1205861.html
   My bibliography  Save this article

Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity

Author

Listed:
  • Lijun Shang

    (School of Quality Management and Standardization, Foshan University, Foshan 528000, China)

  • Baoliang Liu

    (College of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

  • Kaiye Gao

    (School of Economics and Management, Beijing Information Science & Technology University, Beijing 100192, China)

  • Li Yang

    (School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China)

Abstract

Driven by the wide application of industrial software integrated with digital technologies, the real information of task cycles for some products in the real world can be monitored in real time and transmitted to the management center. Monitored task cycles hide consumers’ usage characteristics, which are signals of the products’ usage heterogeneity because they vary from one consumer to another consumer. By classifying monitored task cycles into different categories, this paper customizes two random maintenance models to ensure the life cycle reliability of the product with monitored task cycles on the basis of usage categories. The first model is customized using usage categories, the key objective of which is, from the perspective of heterogeneity, to ensure warranty-stage reliability. In view of using minimal repair service, the first model is named a random free repair warranty with heterogeneity (RFRW-H), which is modeled from the viewpoints of cost and time measures. By calculating the limits of cost and time measures, some specific cases are presented to model other warranties. The second model is customized using the same usage categories, which aims to ensure post-warranty-stage reliability. In view of using each of ‘whichever occurs first/last’, the second model is named a customized random periodic replacement first (CRPRF) model or a customized random periodic replacement last (CRPRL) model, respectively, which are modeled from the viewpoint of the cost rate function. By calculating the limits of the cost rate function, the cost rate functions of other maintenance models are obtained. Finally, from the numerical viewpoint, some of the features of the customized models are mined, and the performances are compared.

Suggested Citation

  • Lijun Shang & Baoliang Liu & Kaiye Gao & Li Yang, 2023. "Random Warranty and Replacement Models Customizing from the Perspective of Heterogeneity," Mathematics, MDPI, vol. 11(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3330-:d:1205861
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3330/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3330/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huang, Yeu-Shiang & Huang, Chao-Da & Ho, Jyh-Wen, 2017. "A customized two-dimensional extended warranty with preventive maintenance," European Journal of Operational Research, Elsevier, vol. 257(3), pages 971-978.
    2. Lijun Shang & Guojun Shang & Qingan Qiu, 2022. "A Bivariate Post-Warranty Maintenance Model for the Product under a 2D Warranty," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    3. Yeh, Ruey Huei & Ho, Wen-Tsung & Tseng, Sheng-Tsaing, 2000. "Optimal production run length for products sold with warranty," European Journal of Operational Research, Elsevier, vol. 120(3), pages 575-582, February.
    4. Lijun Shang & Yongjun Du & Cang Wu & Chengye Ma, 2022. "A Bivariate Optimal Random Replacement Model for the Warranted Product with Job Cycles," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    5. Lijun Shang & Xiguang Yu & Liying Wang & Yongjun Du, 2022. "Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle," Mathematics, MDPI, vol. 10(20), pages 1-22, October.
    6. Wang, Xiaolin & Zhao, Xiujie & Liu, Bin, 2020. "Design and pricing of extended warranty menus based on the multinomial logit choice model," European Journal of Operational Research, Elsevier, vol. 287(1), pages 237-250.
    7. Liu, Bin & Wu, Jun & Xie, Min, 2015. "Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 243(3), pages 874-882.
    8. Gao, Hongda & Cui, Lirong & Yi, He, 2019. "Availability analysis of k-out-of-n: F repairable balanced systems with m sectors," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    9. Xiaopeng Li & Zixian Liu & Yukun Wang & Mei Li, 2019. "Optimal burn-in strategy for two-dimensional warranted products considering preventive maintenance," International Journal of Production Research, Taylor & Francis Journals, vol. 57(17), pages 5414-5431, September.
    10. Wang, Jiantai & Zhou, Shihan & Peng, Rui & Qiu, Qingan & Yang, Li, 2023. "An inspection-based replacement planning in consideration of state-driven imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    11. Chen, Yuan & Qiu, Qingan & Zhao, Xian, 2022. "Condition-based opportunistic maintenance policies with two-phase inspections for continuous-state systems," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    12. Xian Zhao & Rong Li & Yu Fan & Qingan Qiu, 2022. "Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism," Journal of Risk and Reliability, , vol. 236(1), pages 173-193, February.
    13. Qingan Qiu & Lirong Cui & Dejing Kong, 2019. "Availability analysis and optimal inspection policy for systems with neglected down time," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(11), pages 2787-2809, June.
    14. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan & Lin, Cong, 2021. "Optimal condition-based preventive maintenance policy for balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    15. Qiu, Qingan & Cui, Lirong, 2019. "Optimal mission abort policy for systems subject to random shocks based on virtual age process," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 11-20.
    16. Zhuang, Liangliang & Xu, Ancha & Wang, Xiao-Lin, 2023. "A prognostic driven predictive maintenance framework based on Bayesian deep learning," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    17. Qingan Qiu & Lirong Cui, 2019. "Availability analysis for general repairable systems with repair time threshold," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 628-647, February.
    18. Qingan Qiu & Lirong Cui & Jingyuan Shen, 2018. "Availability and maintenance modeling for systems subject to dependent hard and soft failures," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 513-527, July.
    19. Zhao, Xian & Fan, Yu & Qiu, Qingan & Chen, Ke, 2021. "Multi-criteria mission abort policy for systems subject to two-stage degradation process," European Journal of Operational Research, Elsevier, vol. 295(1), pages 233-245.
    20. Lijun Shang & Xiguang Yu & Yongjun Du & Anquan Zou & Qingan Qiu, 2022. "An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    21. Zhi-Sheng Ye & D.N. Murthy & Min Xie & Loon-Ching Tang, 2013. "Optimal burn-in for repairable products sold with a two-dimensional warranty," IISE Transactions, Taylor & Francis Journals, vol. 45(2), pages 164-176.
    22. de Pater, Ingeborg & Reijns, Arthur & Mitici, Mihaela, 2022. "Alarm-based predictive maintenance scheduling for aircraft engines with imperfect Remaining Useful Life prognostics," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    23. Qiu, Qingan & Cui, Lirong & Wu, Bei, 2020. "Dynamic mission abort policy for systems operating in a controllable environment with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    24. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuhan Ma & Fanping Wei & Xiaobing Ma & Qingan Qiu & Li Yang, 2024. "Adaptive Mission Abort Planning Integrating Bayesian Parameter Learning," Mathematics, MDPI, vol. 12(16), pages 1-19, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chengye Ma & Yongjun Du & Lijun Shang & Li Yang & Kaiye Gao, 2023. "Random Maintenance Strategy Modeling of Warranted Products with Reliability Heterogeneity," Sustainability, MDPI, vol. 15(18), pages 1-19, September.
    2. Hui Chen & Jie Chen & Yangyang Lai & Xiaoqi Yu & Lijun Shang & Rui Peng & Baoliang Liu, 2024. "Discrete Random Renewable Replacements after the Expiration of Collaborative Preventive Maintenance Warranty," Mathematics, MDPI, vol. 12(18), pages 1-21, September.
    3. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li & Du, Yongjun, 2023. "Designing warranty and maintenance policies for products subject to random working cycles," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    4. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li, 2023. "Three-dimensional warranty and post-warranty maintenance of products with monitored mission cycles," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    5. Lijun Shang & Xiguang Yu & Yongjun Du & Anquan Zou & Qingan Qiu, 2022. "An Optimal Random Hybrid Maintenance Policy of Systems under a Warranty with Rebate and Charge," Mathematics, MDPI, vol. 10(18), pages 1-19, September.
    6. Lijun Shang & Guojun Shang & Yongjun Du & Qingan Qiu & Li Yang & Qinglai Dong, 2022. "Post-Warranty Replacement Models for the Product under a Hybrid Warranty," Mathematics, MDPI, vol. 10(10), pages 1-18, May.
    7. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    8. Ke Chen & Xian Zhao & Qingan Qiu, 2022. "Optimal Task Abort and Maintenance Policies Considering Time Redundancy," Mathematics, MDPI, vol. 10(9), pages 1-16, April.
    9. Lijun Shang & Xiguang Yu & Liying Wang & Yongjun Du, 2022. "Design of Random Warranty and Maintenance Policy: From a Perspective of the Life Cycle," Mathematics, MDPI, vol. 10(20), pages 1-22, October.
    10. Zhao, Xian & Lv, Zuheng & Qiu, Qingan & Wu, Yaguang, 2023. "Designing two-level rescue depot location and dynamic rescue policies for unmanned vehicles," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    11. Yaguang Wu, 2023. "Optimal Stopping and Loading Rules Considering Multiple Attempts and Task Success Criteria," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    12. Zhao, Xian & Wang, Xinlei & Dai, Ying & Qiu, Qingan, 2024. "Joint optimization of loading, mission abort and rescue site selection policies for UAV," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    13. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Optimal aborting policy for shock exposed missions with random rescue time," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    14. Fang, Chen & Chen, Jianhui & Qiu, Daizhen, 2024. "Reliability modeling for balanced systems considering mission abort policies," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    15. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Optimal mission aborting in multistate systems with storage," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    16. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2022. "Using kamikaze components in multi-attempt missions with abort option," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    17. Yan, Rui & Zhu, Xiaoping & Zhu, Xiaoning & Peng, Rui, 2022. "Optimal routes and aborting strategies of trucks and drones under random attacks," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    18. Liu, Lujie & Yang, Jun & Yan, Bingxin, 2024. "A dynamic mission abort policy for transportation systems with stochastic dependence by deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    19. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    20. Liu, Peng & Wang, Guanjun, 2022. "Minimal repair models with non-negligible repair time," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3330-:d:1205861. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.